Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 8 - Rotational Kinematics - Problems - Page 215: 55

Answer

$\theta=693.6rad$

Work Step by Step

We have the car's initial linear speed $v_0=20m/s$, linear acceleration $a=1.5m/s^2$ and $t=8s$. The wheel's radius $r=0.3m$ In rolling motion, $v=v_T=r\omega$, so the car's initial angular speed is $$\omega_0=\frac{v_0}{r}=66.7rad/s$$ We also have $a=a_T=r\alpha$, so the car's angular acceleration is $$\alpha=\frac{a}{r}=5rad/s^2$$ The angular displacement of each wheel is $$\theta=\omega_0t+\frac{1}{2}\alpha t^2=693.6rad$$
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